Theoretical astrophysics and plasma physics at RPC

Abstract:

ABSTRACT Turbulent, relativistic non-thermal plasmas are ubiquitous in high-energy astrophysical systems, as inferred from broad-band non-thermal emission spectra. The underlying turbulent non-thermal particle acceleration (NTPA) processes have traditionally been modelled with a Fokker–Planck (FP) diffusion–advection equation for the particle energy distribution. We test FP-type NTPA theories by performing and analysing particle-in-cell simulations of turbulence in collisionless relativistic pair plasma. By tracking large numbers of particles in simulations with different initial magnetization and system size, we first test and confirm the applicability of the FP framework. We then measure the FP energy diffusion (D) and advection (A) coefficients as functions of particle energy $\gamma m c^2$, and compare their dependence to theoretical predictions. At high energies, we robustly find $D \sim \gamma ^2$ for all cases. Hence, we fit $D = D_0 \gamma ^2$ and find a scaling consistent with $D_0 \sim \sigma ^{3/2}$ at low instantaneous magnetization $\sigma (t)$, flattening to $D_0 \sim \sigma$ at higher $\sigma \sim 1$. We also find that the power-law index $\alpha (t)$ of the particle energy distribution converges exponentially in time. We build and test an analytic model connecting the FP coefficients and $\alpha (t)$, predicting $A(\gamma) \sim \gamma \log \gamma$. We confirm this functional form in our measurements of $A(\gamma ,t)$, which allows us to predict $\alpha (t)$ through the model relations. Our results suggest that the basic second-order Fermi acceleration model, which predicts $D_0 \sim \sigma$, may not be a complete description of NTPA in turbulent plasmas. These findings encourage further application of tracked particles and FP coefficients as a diagnostic in kinetic simulations of various astrophysically relevant plasma processes like collisionless shocks and magnetic reconnection.

Abstract:

We study the evolution of collisionless plasmas that, due to their macroscopic evolution, are susceptible to the firehose instability, using both analytic theory and hybrid-kinetic particle-in-cell simulations. We establish that, depending on the relative magnitude of the plasma , the characteristic time scale of macroscopic evolution and the ion-Larmor frequency, the saturation of the firehose instability in high- plasmas can result in three qualitatively distinct thermodynamic (and electromagnetic) states. By contrast with the previously identified ‘ultra-high-beta’ and ‘Alfvén-inhibiting’ states, the newly identified ‘Alfvén-enabling’ state, which is realised when the macroscopic evolution time exceeds the ion-Larmor frequency by a -dependent critical parameter, can support linear Alfvén waves and Alfvénic turbulence because the magnetic tension associated with the plasma’s macroscopic magnetic field is never completely negated by anisotropic pressure forces. We characterise these states in detail, including their saturated magnetic-energy spectra. The effective collision operator associated with the firehose fluctuations is also described; we find it to be well approximated in the Alfvén-enabling state by a simple quasi-linear pitch-angle scattering operator. The box-averaged collision frequency is , in agreement with previous results, but certain subpopulations of particles scatter at a much larger (or smaller) rate depending on their velocity in the direction parallel to the magnetic field. Our findings are essential for understanding low-collisionality astrophysical plasmas including the solar wind, the intracluster medium of galaxy clusters and black hole accretion flows. We show that all three of these plasmas are in the Alfvén-enabling regime of firehose saturation and discuss the implications of this result.

Abstract:

The matter power spectrum, $P(k)$ , is one of the fundamental quantities in the study of large-scale structure in cosmology. Here, we study its small-scale asymptotic limit, and show that for cold dark matter in $d$ spatial dimensions, $P(k)$ has a universal $k^{-d}$ asymptotic scaling with the wave number $k$ , for $k\gg k_{\mathrm{nl}}$ , where $k_{\mathrm{nl}}^{-1}$ denotes the length scale at which nonlinearities in gravitational interactions become important. We propose a theoretical explanation for this scaling, based on a nonperturbative analysis of the system’s phase-space structure. Gravitational collapse is shown to drive a turbulent phase-space flow of the quadratic Casimir invariant, where the linear and nonlinear time scales are balanced, and this balance dictates the $k$ dependence of the power spectrum. A parallel is drawn to Batchelor turbulence in hydrodynamics, where large scales mix smaller ones via tidal interactions. The $k^{-d}$ scaling is also derived by expressing $P(k)$ as a phase-space integral in the framework of kinetic field theory, which is analyzed by the saddle-point method; the dominant critical points of this integral are precisely those where the time scales are balanced. The coldness of the dark-matter distribution function—its nonvanishing only on a $d$ -dimensional submanifold of phase space—underpins both approaches. The theory is accompanied by 1D Vlasov-Poisson simulations, which confirm it.

Abstract:

The frequency of compact object interactions in AGN discs is naturally tied to the number of objects embedded within it. We investigate the evolution of black holes in the nuclear stellar cluster on inclined orbits to the AGN disc by performing adiabatic hydrodynamical simulations of isolated black hole disc crossings over a range of disc densities and inclinations . We find radiation dominates the pressure in the wake that forms around the BH across the full inclination and disc density range. We identify no well defined steady state wake morphology due to the thin geometry of the disc and the vertical exponential density drop off, where the wake morphology depends on the vertical depth of the transit within the disc. The inclination damping relative the pre-transit inclination behaves as a power law in and the ambient Hill mass as . The drag on the BH is dominated by the gravity of the wake for the majority of our inclination range until accretion effects become comparable at , where is the disc aspect ratio. At low inclinations () the wake morphology becomes more spherical, leading to a regime change in the inclination damping behaviour. Our results suggest that the inclination damping time-scale is shorter than expected from only episodic Bondi–Hoyle–Lyttelton accretion events during each transit, implying inclined objects may be captured by the AGN disc earlier in its lifetime than previously thought.